Definition:Egyptian Fraction

Definition

An Egyptian fraction is a fraction either:

whose numerator is $1$

or

which is $\dfrac 2 3$

All other fractional quantities are expressed as sums of different Egyptian fractions.

Examples

Egyptian Fraction $\frac 7 {10}$

$\dfrac 7 {10} = \dfrac 2 3 + \dfrac 1 {30}$

Examples of Double Unit Fractions

Egyptian Fraction $\frac 2 7$

$\dfrac 2 7 = \dfrac 1 4 + \dfrac 1 {28}$

Egyptian Fraction $\frac 2 {11}$

$\dfrac 2 {11} = \dfrac 1 6 + \dfrac 1 {66}$

Egyptian Fraction $\frac 2 {97}$

$\dfrac 2 {97} = \dfrac 1 {56} + \dfrac 1 {679} + \dfrac 1 {776}$

Also see

• Definition:Unit Fraction

Historical Note

Egyptian fractions are so called because they were the only means of representations of fractional values in the mathematics of ancient Egypt.

David Wells, in his $1986$ book Curious and Interesting Numbers, refers to $2 / 3$ as "uniquely unrepresentative".

Sources

• 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): Egyptian Fractions
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): Glossary
• 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $1$: Tokens, Tallies and Tablets: The Ancient Egyptians